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Using the GAEA semi-analytic model, we analyse the connection between DampedLyman-$\alpha$ systems (DLAs) and HI in galaxies. Our state-of-the-artsemi-analytic model is tuned to reproduce the local galaxy HI mass function,and that also reproduces other important galaxy properties, including thegalaxy mass - gas metallicity relation. To produce catalogs of simulated DLAswe throw $10^5$ random lines of sight in a composite simulated volume: darkmatter haloes with log$(\frac{M_{200}}{ M_{\odot}}) \geq 11.5$ are extractedfrom the Millennium Simulation, while for $9.2 \leq \log(\frac{M_{200}}{M_{\odot}})<11.5$ we use the Millennium II, and for $8 \leq\log(\frac{M_{200}}{M_{\odot}}) < 9.2$ a halo occupation distribution model. At$2 < z < 3$, where observational data are more accurate, our fiducial modelpredicts the correct shape of the column density distribution function, but itsnormalization falls short of the observations, with the discrepancy increasingat higher redshift. The agreement with observations is significantly improvedincreasing both the HI masses and the disk radii of model galaxies by a factor2, as implemented 'a posteriori' in our $2M-2R$ model. In the redshift range ofinterest, haloes with $M_{200} \geq {10}^{11} M_{\odot}$ give the majorcontribution to $\Omega_{\rm DLA}$, and the typical DLA host halo mass is $\sim{10}^{11} M _{\odot}$. The simulated DLA metallicity distribution is inrelatively good agreement with observations, but our model predicts an excessof DLAs at low metallicities. Our results suggest possible improvements for theadopted modelling of the filtering mass and metal ejection in low-mass haloes.

Damped Lyman-$\alpha$ absorbers and atomic hydrogen in galaxies: the view of the GAEA model